mbed-os 6.10 versione
Diff: cmsis_dsp/TransformFunctions/arm_cfft_radix4_f32.c
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- 1:fdd22bb7aa52
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/cmsis_dsp/TransformFunctions/arm_cfft_radix4_f32.c Wed Nov 28 12:30:09 2012 +0000 @@ -0,0 +1,1236 @@ +/* ---------------------------------------------------------------------- +* Copyright (C) 2010 ARM Limited. All rights reserved. +* +* $Date: 15. February 2012 +* $Revision: V1.1.0 +* +* Project: CMSIS DSP Library +* Title: arm_cfft_radix4_f32.c +* +* Description: Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function +* +* +* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 +* +* Version 1.1.0 2012/02/15 +* Updated with more optimizations, bug fixes and minor API changes. +* +* Version 1.0.10 2011/7/15 +* Big Endian support added and Merged M0 and M3/M4 Source code. +* +* Version 1.0.3 2010/11/29 +* Re-organized the CMSIS folders and updated documentation. +* +* Version 1.0.2 2010/11/11 +* Documentation updated. +* +* Version 1.0.1 2010/10/05 +* Production release and review comments incorporated. +* +* Version 1.0.0 2010/09/20 +* Production release and review comments incorporated. +* +* Version 0.0.5 2010/04/26 +* incorporated review comments and updated with latest CMSIS layer +* +* Version 0.0.3 2010/03/10 +* Initial version +* -------------------------------------------------------------------- */ + +#include "arm_math.h" + +/** + * @ingroup groupTransforms + */ + +/** + * @defgroup Radix4_CFFT_CIFFT Radix-4 Complex FFT Functions + * + * \par + * Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT). + * Computational complexity of CFFT reduces drastically when compared to DFT. + * \par + * This set of functions implements CFFT/CIFFT + * for Q15, Q31, and floating-point data types. The functions operates on in-place buffer which uses same buffer for input and output. + * Complex input is stored in input buffer in an interleaved fashion. + * + * \par + * The functions operate on blocks of input and output data and each call to the function processes + * <code>2*fftLen</code> samples through the transform. <code>pSrc</code> points to In-place arrays containing <code>2*fftLen</code> values. + * \par + * The <code>pSrc</code> points to the array of in-place buffer of size <code>2*fftLen</code> and inputs and outputs are stored in an interleaved fashion as shown below. + * <pre> {real[0], imag[0], real[1], imag[1],..} </pre> + * + * \par Lengths supported by the transform: + * \par + * Internally, the function utilize a radix-4 decimation in frequency(DIF) algorithm + * and the size of the FFT supported are of the lengths [16, 64, 256, 1024]. + * + * + * \par Algorithm: + * + * <b>Complex Fast Fourier Transform:</b> + * \par + * Input real and imaginary data: + * <pre> + * x(n) = xa + j * ya + * x(n+N/4 ) = xb + j * yb + * x(n+N/2 ) = xc + j * yc + * x(n+3N 4) = xd + j * yd + * </pre> + * where N is length of FFT + * \par + * Output real and imaginary data: + * <pre> + * X(4r) = xa'+ j * ya' + * X(4r+1) = xb'+ j * yb' + * X(4r+2) = xc'+ j * yc' + * X(4r+3) = xd'+ j * yd' + * </pre> + * \par + * Twiddle factors for radix-4 FFT: + * <pre> + * Wn = co1 + j * (- si1) + * W2n = co2 + j * (- si2) + * W3n = co3 + j * (- si3) + * </pre> + * + * \par + * \image html CFFT.gif "Radix-4 Decimation-in Frequency Complex Fast Fourier Transform" + * + * \par + * Output from Radix-4 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output. + * \par + * <b> Butterfly CFFT equations:</b> + * <pre> + * xa' = xa + xb + xc + xd + * ya' = ya + yb + yc + yd + * xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) + * yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) + * xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) + * yb' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) + * xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) + * yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) + * </pre> + * + * + * <b>Complex Inverse Fast Fourier Transform:</b> + * \par + * CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below. + * + * \par + * <b> Modified Butterfly CIFFT equations:</b> + * <pre> + * xa' = xa + xb + xc + xd + * ya' = ya + yb + yc + yd + * xc' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) + * yc' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) + * xb' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) + * yb' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) + * xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3) + * yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3) + * </pre> + * + * \par Instance Structure + * A separate instance structure must be defined for each Instance but the twiddle factors and bit reversal tables can be reused. + * There are separate instance structure declarations for each of the 3 supported data types. + * + * \par Initialization Functions + * There is also an associated initialization function for each data type. + * The initialization function performs the following operations: + * - Sets the values of the internal structure fields. + * - Initializes twiddle factor table and bit reversal table pointers + * \par + * Use of the initialization function is optional. + * However, if the initialization function is used, then the instance structure cannot be placed into a const data section. + * To place an instance structure into a const data section, the instance structure must be manually initialized. + * Manually initialize the instance structure as follows: + * <pre> + *arm_cfft_radix4_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen}; + *arm_cfft_radix4_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor}; + *arm_cfft_radix4_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor}; + * </pre> + * \par + * where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT); + * <code>bitReverseFlag</code> Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order); + * <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the array of bit reversal table. + * <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table; + * <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table. + * <code>onebyfftLen</code> value of 1/fftLen to calculate CIFFT; + * + * \par Fixed-Point Behavior + * Care must be taken when using the fixed-point versions of the CFFT/CIFFT function. + * Refer to the function specific documentation below for usage guidelines. + */ + + +/** + * @addtogroup Radix4_CFFT_CIFFT + * @{ + */ + +/** + * @details + * @brief Processing function for the floating-point Radix-4 CFFT/CIFFT. + * @param[in] *S points to an instance of the floating-point Radix-4 CFFT/CIFFT structure. + * @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place. + * @return none. + */ + +void arm_cfft_radix4_f32( + const arm_cfft_radix4_instance_f32 * S, + float32_t * pSrc) +{ + + if(S->ifftFlag == 1u) + { + /* Complex IFFT radix-4 */ + arm_radix4_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle, + S->twidCoefModifier, S->onebyfftLen); + } + else + { + /* Complex FFT radix-4 */ + arm_radix4_butterfly_f32(pSrc, S->fftLen, S->pTwiddle, + S->twidCoefModifier); + } + + if(S->bitReverseFlag == 1u) + { + /* Bit Reversal */ + arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable); + } + +} + + +/** + * @} end of Radix4_CFFT_CIFFT group + */ + + +/* ---------------------------------------------------------------------- +** Internal helper function used by the FFTs +** ------------------------------------------------------------------- */ + +/* + * @brief Core function for the floating-point CFFT butterfly process. + * @param[in, out] *pSrc points to the in-place buffer of floating-point data type. + * @param[in] fftLen length of the FFT. + * @param[in] *pCoef points to the twiddle coefficient buffer. + * @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + * @return none. + */ + +void arm_radix4_butterfly_f32( + float32_t * pSrc, + uint16_t fftLen, + float32_t * pCoef, + uint16_t twidCoefModifier) +{ + + float32_t co1, co2, co3, si1, si2, si3; + uint32_t ia1, ia2, ia3; + uint32_t i0, i1, i2, i3; + uint32_t n1, n2, j, k; + +#ifndef ARM_MATH_CM0 + + /* Run the below code for Cortex-M4 and Cortex-M3 */ + + float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn; + float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc, + Ybminusd; + float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out; + float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out; + float32_t *ptr1; + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2u; + i0 = 0u; + ia1 = 0u; + + j = n2; + + /* Calculation of first stage */ + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + xaIn = pSrc[(2u * i0)]; + yaIn = pSrc[(2u * i0) + 1u]; + + xcIn = pSrc[(2u * i2)]; + ycIn = pSrc[(2u * i2) + 1u]; + + xbIn = pSrc[(2u * i1)]; + ybIn = pSrc[(2u * i1) + 1u]; + + xdIn = pSrc[(2u * i3)]; + ydIn = pSrc[(2u * i3) + 1u]; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + /* xb + xd */ + Xbplusd = xbIn + xdIn; + /* ya + yc */ + Yaplusc = yaIn + ycIn; + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + co2 = pCoef[ia2 * 2u]; + si2 = pCoef[(ia2 * 2u) + 1u]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + /* xb - xd */ + Xbminusd = xbIn - xdIn; + /* ya - yc */ + Yaminusc = yaIn - ycIn; + /* yb + yd */ + Ybminusd = ybIn - ydIn; + + /* xa' = xa + xb + xc + xd */ + pSrc[(2u * i0)] = Xaplusc + Xbplusd; + /* ya' = ya + yb + yc + yd */ + pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd; + + /* (xa - xc) + (yb - yd) */ + Xb12C_out = (Xaminusc + Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yb12C_out = (Yaminusc - Xbminusd); + /* (xa + xc) - (xb + xd) */ + Xc12C_out = (Xaplusc - Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = (Yaplusc - Ybplusd); + /* (xa - xc) - (yb - yd) */ + Xd12C_out = (Xaminusc - Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yd12C_out = (Xbminusd + Yaminusc); + + co1 = pCoef[ia1 * 2u]; + si1 = pCoef[(ia1 * 2u) + 1u]; + + /* index calculation for the coefficients */ + ia3 = ia2 + ia1; + co3 = pCoef[ia3 * 2u]; + si3 = pCoef[(ia3 * 2u) + 1u]; + + Xb12_out = Xb12C_out * co1; + Yb12_out = Yb12C_out * co1; + Xc12_out = Xc12C_out * co2; + Yc12_out = Yc12C_out * co2; + Xd12_out = Xd12C_out * co3; + Yd12_out = Yd12C_out * co3; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + Xb12_out += Yb12C_out * si1; + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + Yb12_out -= Xb12C_out * si1; + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + Xc12_out += Yc12C_out * si2; + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + Yc12_out -= Xc12C_out * si2; + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + Xd12_out += Yd12C_out * si3; + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + Yd12_out -= Xd12C_out * si3; + + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2u * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2u * i1) + 1u] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2u * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2u * i2) + 1u] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2u * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2u * i3) + 1u] = Yd12_out; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + /* Updating input index */ + i0 = i0 + 1u; + + } + while(--j); + + twidCoefModifier <<= 2u; + + /* Calculation of second stage to excluding last stage */ + for (k = fftLen / 4; k > 4u; k >>= 2u) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2u; + ia1 = 0u; + + /* Calculation of first stage */ + for (j = 0u; j <= (n2 - 1u); j++) + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2u]; + si1 = pCoef[(ia1 * 2u) + 1u]; + co2 = pCoef[ia2 * 2u]; + si2 = pCoef[(ia2 * 2u) + 1u]; + co3 = pCoef[ia3 * 2u]; + si3 = pCoef[(ia3 * 2u) + 1u]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + xaIn = pSrc[(2u * i0)]; + yaIn = pSrc[(2u * i0) + 1u]; + + xbIn = pSrc[(2u * i1)]; + ybIn = pSrc[(2u * i1) + 1u]; + + xcIn = pSrc[(2u * i2)]; + ycIn = pSrc[(2u * i2) + 1u]; + + xdIn = pSrc[(2u * i3)]; + ydIn = pSrc[(2u * i3) + 1u]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + /* (xb - xd) */ + Xbminusd = xbIn - xdIn; + /* ya - yc */ + Yaminusc = yaIn - ycIn; + /* (yb - yd) */ + Ybminusd = ybIn - ydIn; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + /* xb + xd */ + Xbplusd = xbIn + xdIn; + /* ya + yc */ + Yaplusc = yaIn + ycIn; + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* (xa - xc) + (yb - yd) */ + Xb12C_out = (Xaminusc + Ybminusd); + /* (ya - yc) - (xb - xd) */ + Yb12C_out = (Yaminusc - Xbminusd); + /* xa + xc -(xb + xd) */ + Xc12C_out = (Xaplusc - Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = (Yaplusc - Ybplusd); + /* (xa - xc) - (yb - yd) */ + Xd12C_out = (Xaminusc - Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yd12C_out = (Xbminusd + Yaminusc); + + pSrc[(2u * i0)] = Xaplusc + Xbplusd; + pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd; + + Xb12_out = Xb12C_out * co1; + Yb12_out = Yb12C_out * co1; + Xc12_out = Xc12C_out * co2; + Yc12_out = Yc12C_out * co2; + Xd12_out = Xd12C_out * co3; + Yd12_out = Yd12C_out * co3; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + Xb12_out += Yb12C_out * si1; + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + Yb12_out -= Xb12C_out * si1; + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + Xc12_out += Yc12C_out * si2; + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + Yc12_out -= Xc12C_out * si2; + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + Xd12_out += Yd12C_out * si3; + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + Yd12_out -= Xd12C_out * si3; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2u * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2u * i1) + 1u] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2u * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2u * i2) + 1u] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2u * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2u * i3) + 1u] = Yd12_out; + + } + } + twidCoefModifier <<= 2u; + } + + j = fftLen >> 2; + ptr1 = &pSrc[0]; + + /* Calculations of last stage */ + do + { + + xaIn = ptr1[0]; + xcIn = ptr1[4]; + yaIn = ptr1[1]; + ycIn = ptr1[5]; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + + xbIn = ptr1[2]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + + xdIn = ptr1[6]; + + /* ya + yc */ + Yaplusc = yaIn + ycIn; + + ybIn = ptr1[3]; + + /* ya - yc */ + Yaminusc = yaIn - ycIn; + + ydIn = ptr1[7]; + + /* xb + xd */ + Xbplusd = xbIn + xdIn; + + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* xa' = xa + xb + xc + xd */ + ptr1[0] = (Xaplusc + Xbplusd); + + /* (xb-xd) */ + Xbminusd = xbIn - xdIn; + + /* ya' = ya + yb + yc + yd */ + ptr1[1] = (Yaplusc + Ybplusd); + + /* (yb-yd) */ + Ybminusd = ybIn - ydIn; + + /* xc' = (xa-xb+xc-xd) */ + ptr1[2] = (Xaplusc - Xbplusd); + /* yc' = (ya-yb+yc-yd) */ + ptr1[3] = (Yaplusc - Ybplusd); + /* xb' = (xa+yb-xc-yd) */ + ptr1[4] = (Xaminusc + Ybminusd); + /* yb' = (ya-xb-yc+xd) */ + ptr1[5] = (Yaminusc - Xbminusd); + /* xd' = (xa-yb-xc+yd)) */ + ptr1[6] = (Xaminusc - Ybminusd); + /* yd' = (ya+xb-yc-xd) */ + ptr1[7] = (Xbminusd + Yaminusc); + + /* increment pointer by 8 */ + ptr1 = ptr1 + 8u; + + } while(--j); + +#else + + float32_t t1, t2, r1, r2, s1, s2; + + /* Run the below code for Cortex-M0 */ + + /* Initializations for the fft calculation */ + n2 = fftLen; + n1 = n2; + for (k = fftLen; k > 1u; k >>= 2u) + { + /* Initializations for the fft calculation */ + n1 = n2; + n2 >>= 2u; + ia1 = 0u; + + /* FFT Calculation */ + for (j = 0u; j <= (n2 - 1u); j++) + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2u]; + si1 = pCoef[(ia1 * 2u) + 1u]; + co2 = pCoef[ia2 * 2u]; + si2 = pCoef[(ia2 * 2u) + 1u]; + co3 = pCoef[ia3 * 2u]; + si3 = pCoef[(ia3 * 2u) + 1u]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* xa + xc */ + r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)]; + + /* xa - xc */ + r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)]; + + /* ya + yc */ + s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u]; + + /* ya - yc */ + s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u]; + + /* xb + xd */ + t1 = pSrc[2u * i1] + pSrc[2u * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2u * i0] = r1 + t1; + + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2u * i0) + 1u] = s1 + t2; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u]; + + /* (xb - xd) */ + t2 = pSrc[2u * i1] - pSrc[2u * i3]; + + /* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */ + pSrc[2u * i1] = (r1 * co2) + (s1 * si2); + + /* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */ + pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2); + + /* (xa - xc) + (yb - yd) */ + r1 = r2 + t1; + + /* (xa - xc) - (yb - yd) */ + r2 = r2 - t1; + + /* (ya - yc) - (xb - xd) */ + s1 = s2 - t2; + + /* (ya - yc) + (xb - xd) */ + s2 = s2 + t2; + + /* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */ + pSrc[2u * i2] = (r1 * co1) + (s1 * si1); + + /* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */ + pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1); + + /* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */ + pSrc[2u * i3] = (r2 * co3) + (s2 * si3); + + /* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */ + pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3); + } + } + twidCoefModifier <<= 2u; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +} + +/* + * @brief Core function for the floating-point CIFFT butterfly process. + * @param[in, out] *pSrc points to the in-place buffer of floating-point data type. + * @param[in] fftLen length of the FFT. + * @param[in] *pCoef points to twiddle coefficient buffer. + * @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. + * @param[in] onebyfftLen value of 1/fftLen. + * @return none. + */ + +void arm_radix4_butterfly_inverse_f32( + float32_t * pSrc, + uint16_t fftLen, + float32_t * pCoef, + uint16_t twidCoefModifier, + float32_t onebyfftLen) +{ + float32_t co1, co2, co3, si1, si2, si3; + uint32_t ia1, ia2, ia3; + uint32_t i0, i1, i2, i3; + uint32_t n1, n2, j, k; + +#ifndef ARM_MATH_CM0 + + float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn; + float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc, + Ybminusd; + float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out; + float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out; + float32_t *ptr1; + + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* n2 = fftLen/4 */ + n2 >>= 2u; + i0 = 0u; + ia1 = 0u; + + j = n2; + + /* Calculation of first stage */ + do + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Butterfly implementation */ + xaIn = pSrc[(2u * i0)]; + yaIn = pSrc[(2u * i0) + 1u]; + + xcIn = pSrc[(2u * i2)]; + ycIn = pSrc[(2u * i2) + 1u]; + + xbIn = pSrc[(2u * i1)]; + ybIn = pSrc[(2u * i1) + 1u]; + + xdIn = pSrc[(2u * i3)]; + ydIn = pSrc[(2u * i3) + 1u]; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + /* xb + xd */ + Xbplusd = xbIn + xdIn; + /* ya + yc */ + Yaplusc = yaIn + ycIn; + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + co2 = pCoef[ia2 * 2u]; + si2 = pCoef[(ia2 * 2u) + 1u]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + /* xb - xd */ + Xbminusd = xbIn - xdIn; + /* ya - yc */ + Yaminusc = yaIn - ycIn; + /* yb - yd */ + Ybminusd = ybIn - ydIn; + + /* xa' = xa + xb + xc + xd */ + pSrc[(2u * i0)] = Xaplusc + Xbplusd; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd; + + /* (xa - xc) - (yb - yd) */ + Xb12C_out = (Xaminusc - Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yb12C_out = (Yaminusc + Xbminusd); + /* (xa + xc) - (xb + xd) */ + Xc12C_out = (Xaplusc - Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = (Yaplusc - Ybplusd); + /* (xa - xc) + (yb - yd) */ + Xd12C_out = (Xaminusc + Ybminusd); + /* (ya - yc) - (xb - xd) */ + Yd12C_out = (Yaminusc - Xbminusd); + + co1 = pCoef[ia1 * 2u]; + si1 = pCoef[(ia1 * 2u) + 1u]; + + /* index calculation for the coefficients */ + ia3 = ia2 + ia1; + co3 = pCoef[ia3 * 2u]; + si3 = pCoef[(ia3 * 2u) + 1u]; + + Xb12_out = Xb12C_out * co1; + Yb12_out = Yb12C_out * co1; + Xc12_out = Xc12C_out * co2; + Yc12_out = Yc12C_out * co2; + Xd12_out = Xd12C_out * co3; + Yd12_out = Yd12C_out * co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + Xb12_out -= Yb12C_out * si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + Yb12_out += Xb12C_out * si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + Xc12_out -= Yc12C_out * si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + Yc12_out += Xc12C_out * si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + Xd12_out -= Yd12C_out * si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + Yd12_out += Xd12C_out * si3; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2u * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2u * i1) + 1u] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2u * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2u * i2) + 1u] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2u * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2u * i3) + 1u] = Yd12_out; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + /* Updating input index */ + i0 = i0 + 1u; + + } while(--j); + + twidCoefModifier <<= 2u; + + /* Calculation of second stage to excluding last stage */ + for (k = fftLen / 4; k > 4u; k >>= 2u) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2u; + ia1 = 0u; + + /* Calculation of first stage */ + for (j = 0u; j <= (n2 - 1u); j++) + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2u]; + si1 = pCoef[(ia1 * 2u) + 1u]; + co2 = pCoef[ia2 * 2u]; + si2 = pCoef[(ia2 * 2u) + 1u]; + co3 = pCoef[ia3 * 2u]; + si3 = pCoef[(ia3 * 2u) + 1u]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + xaIn = pSrc[(2u * i0)]; + yaIn = pSrc[(2u * i0) + 1u]; + + xbIn = pSrc[(2u * i1)]; + ybIn = pSrc[(2u * i1) + 1u]; + + xcIn = pSrc[(2u * i2)]; + ycIn = pSrc[(2u * i2) + 1u]; + + xdIn = pSrc[(2u * i3)]; + ydIn = pSrc[(2u * i3) + 1u]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + /* (xb - xd) */ + Xbminusd = xbIn - xdIn; + /* ya - yc */ + Yaminusc = yaIn - ycIn; + /* (yb - yd) */ + Ybminusd = ybIn - ydIn; + + /* xa + xc */ + Xaplusc = xaIn + xcIn; + /* xb + xd */ + Xbplusd = xbIn + xdIn; + /* ya + yc */ + Yaplusc = yaIn + ycIn; + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* (xa - xc) - (yb - yd) */ + Xb12C_out = (Xaminusc - Ybminusd); + /* (ya - yc) + (xb - xd) */ + Yb12C_out = (Yaminusc + Xbminusd); + /* xa + xc -(xb + xd) */ + Xc12C_out = (Xaplusc - Xbplusd); + /* (ya + yc) - (yb + yd) */ + Yc12C_out = (Yaplusc - Ybplusd); + /* (xa - xc) + (yb - yd) */ + Xd12C_out = (Xaminusc + Ybminusd); + /* (ya - yc) - (xb - xd) */ + Yd12C_out = (Yaminusc - Xbminusd); + + pSrc[(2u * i0)] = Xaplusc + Xbplusd; + pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd; + + Xb12_out = Xb12C_out * co1; + Yb12_out = Yb12C_out * co1; + Xc12_out = Xc12C_out * co2; + Yc12_out = Yc12C_out * co2; + Xd12_out = Xd12C_out * co3; + Yd12_out = Yd12C_out * co3; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + Xb12_out -= Yb12C_out * si1; + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + Yb12_out += Xb12C_out * si1; + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + Xc12_out -= Yc12C_out * si2; + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + Yc12_out += Xc12C_out * si2; + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + Xd12_out -= Yd12C_out * si3; + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + Yd12_out += Xd12C_out * si3; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2u * i1] = Xc12_out; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2u * i1) + 1u] = Yc12_out; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2u * i2] = Xb12_out; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2u * i2) + 1u] = Yb12_out; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2u * i3] = Xd12_out; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2u * i3) + 1u] = Yd12_out; + + } + } + twidCoefModifier <<= 2u; + } + /* Initializations of last stage */ + + j = fftLen >> 2; + ptr1 = &pSrc[0]; + + /* Calculations of last stage */ + do + { + + xaIn = ptr1[0]; + xcIn = ptr1[4]; + yaIn = ptr1[1]; + ycIn = ptr1[5]; + + /* Butterfly implementation */ + /* xa + xc */ + Xaplusc = xaIn + xcIn; + + xbIn = ptr1[2]; + + /* xa - xc */ + Xaminusc = xaIn - xcIn; + + xdIn = ptr1[6]; + + /* ya + yc */ + Yaplusc = yaIn + ycIn; + + ybIn = ptr1[3]; + + /* ya - yc */ + Yaminusc = yaIn - ycIn; + + ydIn = ptr1[7]; + + /* xc + xd */ + Xbplusd = xbIn + xdIn; + + /* yb + yd */ + Ybplusd = ybIn + ydIn; + + /* xa' = xa + xb + xc + xd */ + ptr1[0] = (Xaplusc + Xbplusd) * onebyfftLen; + + /* (xb-xd) */ + Xbminusd = xbIn - xdIn; + + /* ya' = ya + yb + yc + yd */ + ptr1[1] = (Yaplusc + Ybplusd) * onebyfftLen; + + /* (yb-yd) */ + Ybminusd = ybIn - ydIn; + + /* xc' = (xa-xb+xc-xd) * onebyfftLen */ + ptr1[2] = (Xaplusc - Xbplusd) * onebyfftLen; + + /* yc' = (ya-yb+yc-yd) * onebyfftLen */ + ptr1[3] = (Yaplusc - Ybplusd) * onebyfftLen; + + /* xb' = (xa-yb-xc+yd) * onebyfftLen */ + ptr1[4] = (Xaminusc - Ybminusd) * onebyfftLen; + + /* yb' = (ya+xb-yc-xd) * onebyfftLen */ + ptr1[5] = (Yaminusc + Xbminusd) * onebyfftLen; + + /* xd' = (xa-yb-xc+yd) * onebyfftLen */ + ptr1[6] = (Xaminusc + Ybminusd) * onebyfftLen; + + /* yd' = (ya-xb-yc+xd) * onebyfftLen */ + ptr1[7] = (Yaminusc - Xbminusd) * onebyfftLen; + + /* increment source pointer by 8 for next calculations */ + ptr1 = ptr1 + 8u; + + } while(--j); + +#else + + float32_t t1, t2, r1, r2, s1, s2; + + /* Run the below code for Cortex-M0 */ + + /* Initializations for the first stage */ + n2 = fftLen; + n1 = n2; + + /* Calculation of first stage */ + for (k = fftLen; k > 4u; k >>= 2u) + { + /* Initializations for the first stage */ + n1 = n2; + n2 >>= 2u; + ia1 = 0u; + + /* Calculation of first stage */ + for (j = 0u; j <= (n2 - 1u); j++) + { + /* index calculation for the coefficients */ + ia2 = ia1 + ia1; + ia3 = ia2 + ia1; + co1 = pCoef[ia1 * 2u]; + si1 = pCoef[(ia1 * 2u) + 1u]; + co2 = pCoef[ia2 * 2u]; + si2 = pCoef[(ia2 * 2u) + 1u]; + co3 = pCoef[ia3 * 2u]; + si3 = pCoef[(ia3 * 2u) + 1u]; + + /* Twiddle coefficients index modifier */ + ia1 = ia1 + twidCoefModifier; + + for (i0 = j; i0 < fftLen; i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* xa + xc */ + r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)]; + + /* xa - xc */ + r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)]; + + /* ya + yc */ + s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u]; + + /* ya - yc */ + s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u]; + + /* xb + xd */ + t1 = pSrc[2u * i1] + pSrc[2u * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2u * i0] = r1 + t1; + + /* xa + xc -(xb + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2u * i0) + 1u] = s1 + t2; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb - yd) */ + t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u]; + + /* (xb - xd) */ + t2 = pSrc[2u * i1] - pSrc[2u * i3]; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2u * i1] = (r1 * co2) - (s1 * si2); + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2); + + /* (xa - xc) - (yb - yd) */ + r1 = r2 - t1; + + /* (xa - xc) + (yb - yd) */ + r2 = r2 + t1; + + /* (ya - yc) + (xb - xd) */ + s1 = s2 + t2; + + /* (ya - yc) - (xb - xd) */ + s2 = s2 - t2; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2u * i2] = (r1 * co1) - (s1 * si1); + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1); + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2u * i3] = (r2 * co3) - (s2 * si3); + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3); + } + } + twidCoefModifier <<= 2u; + } + /* Initializations of last stage */ + n1 = n2; + n2 >>= 2u; + + /* Calculations of last stage */ + for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1) + { + /* index calculation for the input as, */ + /* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */ + i1 = i0 + n2; + i2 = i1 + n2; + i3 = i2 + n2; + + /* Butterfly implementation */ + /* xa + xc */ + r1 = pSrc[2u * i0] + pSrc[2u * i2]; + + /* xa - xc */ + r2 = pSrc[2u * i0] - pSrc[2u * i2]; + + /* ya + yc */ + s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u]; + + /* ya - yc */ + s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u]; + + /* xc + xd */ + t1 = pSrc[2u * i1] + pSrc[2u * i3]; + + /* xa' = xa + xb + xc + xd */ + pSrc[2u * i0] = (r1 + t1) * onebyfftLen; + + /* (xa + xb) - (xc + xd) */ + r1 = r1 - t1; + + /* yb + yd */ + t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u]; + + /* ya' = ya + yb + yc + yd */ + pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen; + + /* (ya + yc) - (yb + yd) */ + s1 = s1 - t2; + + /* (yb-yd) */ + t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u]; + + /* (xb-xd) */ + t2 = pSrc[2u * i1] - pSrc[2u * i3]; + + /* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */ + pSrc[2u * i1] = r1 * onebyfftLen; + + /* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */ + pSrc[(2u * i1) + 1u] = s1 * onebyfftLen; + + + /* (xa - xc) - (yb-yd) */ + r1 = r2 - t1; + + /* (xa - xc) + (yb-yd) */ + r2 = r2 + t1; + + /* (ya - yc) + (xb-xd) */ + s1 = s2 + t2; + + /* (ya - yc) - (xb-xd) */ + s2 = s2 - t2; + + /* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */ + pSrc[2u * i2] = r1 * onebyfftLen; + + /* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */ + pSrc[(2u * i2) + 1u] = s1 * onebyfftLen; + + /* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */ + pSrc[2u * i3] = r2 * onebyfftLen; + + /* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */ + pSrc[(2u * i3) + 1u] = s2 * onebyfftLen; + } + +#endif /* #ifndef ARM_MATH_CM0 */ + +}